This paper proposes a dynamic controller design technique based on super-twisting sliding mode control (STSMC) and observation to enhance the precision of a differential-drive mobile robot (DDMR) trajectory tracking in the presence of uncertainties and external disturbances. Firstly, a more dynamic model is developed by introducing the load and friction between the wheels and the road surface. The load includes the additional payload being transported and the mass of the DDMR. Second, a state observer is designed to estimate the system’s unmeasured velocities, which are critical for controller design. Thirdly, a trajectory tracking controller integrating an observer with an STSMC is designed to ensure system stability by guaranteeing asymptotic convergence to both the desired trajectory and necessary velocities. Finally, the designed controller was compared with an existing version of the super-twist controller to demonstrate its efficiency. The research results have important implications for designing dynamic controllers for DDMR to achieve high trajectory tracking accuracy at a certain velocity.